Eliminate a group from the email to members

I have 6 groups that have blogs and media galleries.  When new blogs or media are added to the community I would like to send out a monthly email to all users to 'check out the new content' or highlight a specific blog.  However I would like to exclude 1 of the groups from this logic.  Is there a way to exclude a group in this way?

My thought was to customize the master email template or the email digest to exclude that group by some type of identifier?

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